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--- 184_notes:examples:week2_electric_potential_negative_point [2017/08/25 20:38] – tallpaul
+++ 184_notes:examples:week2_electric_potential_negative_point [2018/05/17 16:49] (current) – curdemma
@@ Line 1: / Line 1: @@
-===== Example: Electric Potential from a Negative Point Charge =====
+[[184_notes:pc_potential|Return to Electric Potential]]
-Suppose we have a negative point charge with charge $-Q$. What is the electric potential at a point $P$, which is a distance $R$ from the point charge?
+===== Example: Electric Potential from a Negatively Charged Balloon =====
-{{ 184_notes:2_potential_negative_point.png?150 |Negative Point Charge -Q, and Point P}}
+Suppose we have a negatively charged balloon with total charge $Q=-5.0\cdot 10^{-9} \text{ C}$. What is the electric potential (also called voltage) at a point $P$, which is a distance $R=20 \text{ m}$ from the center of the balloon?
 ===Facts===
-  * The charge with value $-Q$ is a point charge.
+  * The balloon has total charge $Q=-5.0\cdot 10^{-9} \text{ C}$.
-  * The point $P$ is a distance $R$ away from the point charge.
+  * The point $P$ is a distance $R=20 \text{ m}$ away from the center of the balloon.
+  * The electric potential due to a point charge can be written as $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r},$$ where $q$ represents the charge and $r$ is the distance.
-===Lacking===
-  * The electric potential at $P$.
-===Approximations & Assumptions===
-  * The electric potential at $P$ is due entirely to the point charge.
-  * The electric potential infinitely far away from the point charge is $0 \text{ V}$.
 ===Representations===
-  * The electric potential from the point charge can be written as $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r},$$ where $q$ represents our charge ($-Q$) and $r$ is our distance ($R$).
+<WRAP TIP>
+=== Assumption ===
+We assume $P$ lies outside of the balloon. This is obvious, as $P$ is a distance $R=20 \text{ m}$ away from the center of the balloon.
+</WRAP>
+[{{ 184_notes:2_potential_positive_balloon.png?150 |Charged Balloon, and Point P}}]
+===Goal===
+  * Find the electric potential at $P$.
 ====Solution====
+<WRAP TIP>
+=== Approximation ===
+We approximate the balloon as a point charge. We do this because we have the tools to find the electric potential from a point charge. This seems like a reasonable approximation because the balloon is not too spread out, and we are interested in a point very far from the balloon, so the balloon would "look" like a point charge from the perspective of an observation location that is $20 \text{ m}$ away.
+</WRAP>
+<WRAP TIP>
+=== Assumption ===
+The electric potential infinitely far away from the balloon is $0 \text{ V}$. Read [[184_notes:superposition#Superposition_of_Electric_Potential|here]] for why this is important.
+</WRAP>
 The electric potential at $P$ is given by
 \begin{align*}
 V &= \frac{1}{4\pi\epsilon_0}\frac{q}{r} \\
-  &= \frac{1}{4\pi\epsilon_0}\frac{(-Q)}{R} \\
+  &= \frac{1}{4\pi\cdot 8.85\cdot 10^{-12} \frac{\text{C}}{\text{Vm}}}\frac{-5.0\cdot 10^{-9} \text{ C}}{20 \text{ m}} \\
-  &= -\frac{1}{4\pi\epsilon_0}\frac{Q}{R}
+  &= -2.2 \text{ V}
 \end{align*}
+Notice how the magnitude of charge on the balloon is the same as in the "positively charged balloon" [[184_notes:examples:Week2_electric_potential_positive_point|example]]. The reason the magnitude of the voltage is so much smaller, is because the distance is so much greater. [[184_notes:pc_potential#Potential_vs_Distance_Graphs|The closer you get to a point charge, the higher the magnitude of electric potential]].